The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1
 0  X  0  0  0  0  X  X  X a*X  0  X a^2*X a*X  X a*X a*X  X a^2*X  X a^2*X  X  0 a^2*X a^2*X  X a*X a*X a^2*X  0  X a*X  0
 0  0  X  0  0  X a^2*X a*X a*X a*X  0  0 a*X a*X  0 a*X a^2*X a*X  0  X a*X a*X  X a^2*X  X a^2*X  0  X a*X a^2*X  0  X a^2*X
 0  0  0  X  0 a^2*X  0  X a*X a^2*X  X  X  X  0  X a^2*X a^2*X  X  0  X a*X a^2*X a^2*X  0 a*X  0 a*X a*X  0  X a^2*X a*X a^2*X
 0  0  0  0  X  X  X a^2*X  X  X  X a*X  0  0  0 a*X a^2*X a*X  X  0  0  X a*X a*X  0 a*X a*X  X a^2*X a^2*X  X a^2*X a*X

generates a code of length 33 over F4[X]/(X^2) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+225x^88+165x^92+921x^96+2382x^100+165x^104+78x^108+75x^112+54x^116+18x^120+9x^124+3x^128

The gray image is a linear code over GF(4) with n=132, k=6 and d=88.
This code was found by Heurico 1.16 in 97.4 seconds.